Reverse M-Polynomial-Based QSPR Analysis of Antidiabetic Drugs

Non-communicable diseases (NCDs), particularly diabetes mellitus, motivate the mathematical investigation of drug-related molecular systems through rigorous structural descriptors. Within the framework of chemical graph theory, this study develops a quantitative structure–property relationship (QSPR) analysis for antidiabetic drug candidates based on reverse M-polynomial–derived invariants. Molecular structures of sixteen clinically relevant antidiabetic drugs are modeled as simple connected graphs, and their reverse M-polynomials are constructed via edge partitioning with respect to reverse vertex degrees. Using operator-based techniques, a family of reverse degree-based topological indices is systematically derived from these generating polynomials. Linear, quadratic, and cubic regression models are employed to examine the dependence of key physicochemical properties—namely boiling point (BP), enthalpy (E), flash point (FP), molar refractivity (MR), and polarizability (P)—on the proposed graph invariants. Statistical evaluation based on the coefficient of determination (R۲), standard error, and F-statistics (F) reveals that several reverse descriptors exhibit strong and statistically significant correlations with the investigated properties. In particular, the reverse symmetric division degree index (RSDD) shows the strongest correlations with thermal properties (BP, E, and FP), whereas the reverse geometric–arithmetic index (RGA) performs best for electronic properties such as MR and P. Comparative analysis across regression orders further indicates that linear models provide the most balanced and interpretable representation of the structure–property relationships. Overall, the results demonstrate that reverse M-polynomial–based topological indices encode meaningful graph-theoretical information and provide a consistent mathematical framework for theoretical QSPR studies of molecular systems associated with NCDs.

کلیدواژه ها:

non-communicable diseases ، Antidiabetic drugs ، Reverse M-polynomial ، QSPR analysis